Displaying similar documents to “Selivanovski hard sets are hard”

Some properties of algebras of real-valued measurable functions

Ali Akbar Estaji, Ahmad Mahmoudi Darghadam (2023)

Archivum Mathematicum

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Let M ( X , 𝒜 ) ( M * ( X , 𝒜 ) ) be the f -ring of all (bounded) real-measurable functions on a T -measurable space ( X , 𝒜 ) , let M K ( X , 𝒜 ) be the family of all f M ( X , 𝒜 ) such that coz ( f ) is compact, and let M ( X , 𝒜 ) be all f M ( X , 𝒜 ) that { x X : | f ( x ) | 1 n } is compact for any n . We introduce realcompact subrings of M ( X , 𝒜 ) , we show that M * ( X , 𝒜 ) is a realcompact subring of M ( X , 𝒜 ) , and also M ( X , 𝒜 ) is a realcompact if and only if ( X , 𝒜 ) is a compact measurable space. For every nonzero real Riesz map ϕ : M ( X , 𝒜 ) , we prove that there is an element x 0 X such that ϕ ( f ) = f ( x 0 ) for every f M ( X , 𝒜 ) if ( X , 𝒜 ) is a compact measurable space....

A localization property for B p q s and F p q s spaces

Hans Triebel (1994)

Studia Mathematica

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Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

C * -points vs P -points and P -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

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In a Tychonoff space X , the point p X is called a C * -point if every real-valued continuous function on C { p } can be extended continuously to p . Every point in an extremally disconnected space is a C * -point. A classic example is the space 𝐖 * = ω 1 + 1 consisting of the countable ordinals together with ω 1 . The point ω 1 is known to be a C * -point as well as a P -point. We supply a characterization of C * -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

Selectors of discrete coarse spaces

Igor Protasov (2022)

Commentationes Mathematicae Universitatis Carolinae

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Given a coarse space ( X , ) with the bornology of bounded subsets, we extend the coarse structure from X × X to the natural coarse structure on ( { } ) × ( { } ) and say that a macro-uniform mapping f : ( { } ) X (or f : [ X ] 2 X ) is a selector (or 2-selector) of ( X , ) if f ( A ) A for each A { } ( A [ X ] 2 , respectively). We prove that a discrete coarse space ( X , ) admits a selector if and only if ( X , ) admits a 2-selector if and only if there exists a linear order “ " on X such that the family of intervals { [ a , b ] : a , b X , a b } is a base for the bornology .

Σ s -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

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We show that any Σ s -product of at most 𝔠 -many L Σ ( ω ) -spaces has the L Σ ( ω ) -property. This result generalizes some known results about L Σ ( ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

Spaces with property ( D C ( ω 1 ) )

Wei-Feng Xuan, Wei-Xue Shi (2017)

Commentationes Mathematicae Universitatis Carolinae

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We prove that if X is a first countable space with property ( D C ( ω 1 ) ) and with a G δ -diagonal then the cardinality of X is at most 𝔠 . We also show that if X is a first countable, DCCC, normal space then the extent of X is at most 𝔠 .

Theoretical analysis for 1 - 2 minimization with partial support information

Haifeng Li, Leiyan Guo (2025)

Applications of Mathematics

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We investigate the recovery of k -sparse signals using the 1 - 2 minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume k -sparse signals 𝐱 with the prior support T which is composed of g true indices and b wrong...

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

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In this paper we prove the following theorems in incidence geometry. 1. There is δ > 0 such that for any P 1 , , P 4 , and Q 1 , , Q n 2 , if there are n ( 1 + δ ) / 2 many distinct lines between P i and Q j for all i , j , then P 1 , , P 4 are collinear. If the number of the distinct lines is < c n 1 / 2 then the cross ratio of the four points is algebraic. 2. Given c > 0 , there is δ > 0 such that for any P 1 , P 2 , P 3 2 noncollinear, and Q 1 , , Q n 2 , if there are c n 1 / 2 many distinct lines between P i and Q j for all i , j , then for any P 2 { P 1 , P 2 , P 3 } , we have δ n distinct lines between P and Q j . 3. Given...